Sharp vertices in model
Ok. I played some with your model. It seems during modeling some edges became corrupt. What you need to do is select all the offending edges, that should be smoothed by SDS but are not, one by one, hit X choose Dissolve Edge, then select the 2 remaining Vertices and hit J. What you will be doing is in fact replacing all erronous existing edges with new ones. Then they become smooth under SDS. Then you can apply Crease to all the needed edges. It's a laborious task, but it works. You need to rebuild all the corrupt edges one by one.

Here I rebuilt 2 edges, as an example.